Triangulation-Based Approaches to Three-Dimensional Scene Reconstruction - 3D Computer Vision: Efficient Methods and Applications - page 67

performs similarly to classical stereo vision approaches that do not go into the tem-
poral domain, but it requires smaller matching windows.
The spacetime stereo framework described by Davis et al. ( 2005 ) is fairly simi-
lar to the one presented by Zhang et al. ( 2003 ). However, the spatial and temporal
derivatives of the disparity are not estimated. Davis et al. ( 2005 ) concentrate on the
determination of the optimal spatio-temporal size of the matching window for static
scenes and scenes with moving objects. For static scenes illuminated with tempo-
rally variable but not strictly controlled structured light patterns, they conclude that
after acquiring only a short sequence of about 25 images, it is no longer neces-
sary to use spatially extended matching windows, since a purely temporal matching
vector turns out to yield the highest reconstruction accuracy. Scenes with linearly
moving and with rotating objects are illuminated with light patterns varying at high
frequency, generated with an uncalibrated LCD projector. Davis et al. ( 2005 ) find
that the optimum temporal window size is smaller and the optimum spatial window
size is larger for a scene with a linearly moving object than for a scene displaying
a rotating object. The optimum temporal extension decreases with increasing speed
of the motion. For illumination with a temporally variable light pattern, Davis et al.
( 2005 ) conclude that for scenes with very fast motion, purely spatial stereo analysis
is favourable, while static scenes should be analysed based on the purely temporal
variations of the pixel grey values.
For obstacle avoidance in the context of driver assistance and mobile robotic
systems, which require an extraction of depth information and the robust and fast
detection of moving objects, Franke et al. ( 2005 ) introduce a framework termed
6D vision, addressing the integration of stereo and optical flow. For each individ-
ual extracted scene point, the three-dimensional world coordinates and the three-
dimensional velocity vector are determined based on Kalman filters. Vedula et al.
( 2005 ) introduce the concept of scene flow, which contains the three-dimensional
positions of the scene points along with their three-dimensional velocities. Hence,
projecting the scene flow into the image plane yields the classical two-dimensional
optical flow. Therefore, the 6D vision method by Franke et al. ( 2005 ) yields sparse
scene flow information. Huguet and Devernay ( 2007 ) determine dense scene flow
using an integrated simultaneous determination of the optical flow in both stereo
images and a dense disparity map (cf. Fig. 1.22 ). A variational approach yields a
system of partial differential equations that simultaneously determine the dispari-
ties and the optical flow field, which allows the method to cope with discontinuities
of the disparities and the three-dimensional velocity field. Applying this method to
multiple resolution levels eventually yields a numerical solution of the partial differ-
ential equations. While previous variational approaches, e.g. by Pons et al. ( 2005 ),
estimate the three-dimensional scene point coordinates and the three-dimensional
velocity field separately, they are computed simultaneously in a single adjustment
stage by Huguet and Devernay ( 2007 ).
A computationally very efficient method for the computation of the scene flow
is introduced by Wedel et al. ( 2008a , 2008b ) and is refined and extended by Wedel
et al. ( 2011 ). In contrast to Huguet and Devernay ( 2007 ), who determine the scene
flow in an integrated manner by an optimisation of the disparity and the optical flow